After a post-Fed battering, markets head into the week ahead seeking clarity, especially from two key people—Janet Yellen and Xi Jinping.

Fed Chair Jane Yellen speaks at the University of Massachusetts on Thursday evening, and Chinese President Xi Jinping will be in the U.S., meeting with business leaders Wednesday and President Barack Obama on Thursday. Both Xi and Yellen could offer some reassurance on what ails markets—the fear that economic growth and financial weakness in China is worse than expected and that it could spread elsewhere, including to the U.S.

Brendan McDermid | Reuters

Traders work on the floor of the New York Stock Exchange.

Stocks were crushed Friday after the Fed held off hiking rates Thursday, saying it was concerned that global and financial developments could hurt the economy and drive inflation even lower in the near term.

The S&P 500 lost 32 points Friday to 1,958, a 1.6 percent decline, but it ended down just 0.2 percent for the week. Market strategists expect the volatility to continue for now, and some say it would not be difficult to see the S&P 500 revisiting its low of 1,867 set in August.

"It's certainly a possibility particularly as we go toward another round of negative earnings revisions, as we go into the next earnings season. I think we're very dependent on the data flows as it comes out on the domestic economy. The Fed announcement was just another wake-up call that we're not in the clear and the market in the last couple of weeks traded like maybe we started to clear the concerns, but it's not over yet," said Gina Martin Adams, institutional equity strategist at Wells Fargo Securities. "We expect the market to stay very volatile and we have another Fed meeting in a month ... until we get clarity stocks remain volatile, and probably trade sideways at best."

Besides Fed speak and China, markets will be watching the U.S. data calendar. Existing home sales are reported Monday, and new home sales are Thursday. There are durable goods Thursday, and consumer sentiment and the final revision to second-quarter GDP on Friday.

"It's jampacked next week. You get a little housing, a little consumer, a little industrial. That could be market moving. I suspect the U.S. data is not going to show any weakness coming from overseas, so investors are going to be focused more on any data from China," said Adams. The next piece of Chinese data are leading indicators Tuesday.

Other Fed officials will be speaking ahead of Yellen's Thursday appearance, including St. Louis Fed President James Bullard who appears on CNBC's "Squawk Box" on Monday for two hours, beginning at 7 a.m. ET.

Yellen said the Fed could still hike rates this year, but markets were also concerned that it downgraded its view of U.S. growth and trimmed inflation expectations. As for Yellen, markets will look for reassurances from her on the U.S. economy, although she emphasized it was doing well when she spoke Thursday. Markets were shaken by the Fed's concerns that China could have a broader economic impact, even though markets were already rocked this summer by those same fears.

""The Fed speaking calendar comes to life, but not as much as it should because there's a lack of clarity," said Jefferies money market economist Tom Simons.

"Their lack of clarity is one reason the market is acting the way it is. If they had communicated the rate hike was not a strong possibility, things would be easier to swallow today," he said.

Simons has been expecting a December rate hike. "On the margin, this makes it a little less likely they would go in December. Frankly, they were significantly more dovish than I had anticipated. You think about what needs to happen between now and then, in order for concerns to be mitigated, you need things to get better in a hurry," he said. "I don't know if three months is enough time to determine whether negative forces have abated."

As for Xi, Simons said he is watching for any comments on the economy; he will even be watching the Chinese leader's body language.

"If the Fed were just dealing with the U.S. economy in a vacuum they could have raised rates any time," he said. "What's keeping them from doing that is commodity prices."

The worry has been that China's slowing will filter through to the U.S. economy via emerging markets as well as bringing deflation from falling commodities prices. JPMorgan economists in a report said a 1 percent GDP shock in China equates to a half-point drag on global growth. The hit on emerging markets is one for one, but the drag on development markets is more like 0.2 percent, according to JPMorgan.

JPMorgan international economist David Hensley does not expect to get much more insight from Xi but he will be following him, as he moves from Seattle to Washington.

"Obviously, everybody's keen to understand better what's happening with growth and policy in China, and I'm sure this is going to come up both in the business meetings and with the president, and if he (Xi) does have a press conference," said Hensley. "I think they've tried to deal with this issue already in other forums, including the G-20 meeting, to try to reassure that they're not doing anything radical with regards to their currency, which is a sore point, not only here but in Asia."

China has been looking to reform policy but it has been criticized for using a heavy hand in markets it is trying to open up, and traders have been skeptical that the country's economic reports are not trustworthy.

"One of his important messages is going to be just to reassure people that the Chinese economy is slower but not weak and is not a source of instability, and that policymakers have a steady hand and know what they're doing. Are we going to learn anything from that? Probably not. It's more about tone. Does he establish the confidence that's been missing up to now?" said Hensley.